In contrast to the non-supersymmetric case, explicit expressions for the higher-spin super-Cotton tensors are easily obtained in \(\mathcal {N}=1\)  AdS superspace. In [1]}, some of the lower rank super-Cotton tensors were derived using the operator
\(\Delta ^{\alpha }{}_{\beta }:=-\frac{\text{i}}{2}\mathcal {D}^{\alpha }\mathcal {D}_{\beta }-2\mathcal {S}\delta ^{\alpha }{}_{\beta } \) 
